Number Sequences | Interactive Worksheet - Free Printable
Educational worksheet: Number Sequences | Interactive Worksheet. Download and print for classroom or home learning activities.
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Step-by-step solution for: Number Sequences | Interactive Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Number Sequences | Interactive Worksheet
Let’s solve each number sequence one by one. We’ll look for the pattern — like adding, subtracting, multiplying, or dividing — and then fill in the missing number.
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1. 2, 4, __, 8
Look: 2 to 4 is +2. Then 4 to ? should be +2 → 6. Then 6 to 8 is +2. ✔
→ Missing: 6
2. 1, 5, __, 13
1 to 5 is +4. 5 to ? should be +4 → 9. 9 to 13 is +4. ✔
→ Missing: 9
3. 3, 6, __, 12
3 to 6 is +3. 6 to ? should be +3 → 9. 9 to 12 is +3. ✔
→ Missing: 9
4. 5, __, 15, 20
5 to ? to 15 to 20. From 15 to 20 is +5. So before that, ? to 15 should also be +5 → ? = 10. Check: 5 to 10 is +5. ✔
→ Missing: 10
5. 1, __, 9, 27
Hmm… 1 to ? to 9 to 27. Looks like multiplying by 3?
1 × 3 = 3 → 3 × 3 = 9 → 9 × 3 = 27. Perfect!
→ Missing: 3
6. 4, __, 16, 32
4 to ? to 16 to 32. Let’s see: 16 to 32 is ×2. So ? to 16 should be ×2 → ? = 8. Check: 4 to 8 is ×2. ✔
→ Missing: 8
7. 6, 8, __, 20
6 to 8 is +2. If we keep +2: 8 + 2 = 10, then 10 + 2 = 12… but next is 20? That doesn’t fit.
Wait — maybe it’s increasing by even numbers?
6 + 2 = 8
8 + 4 = 12
12 + 8 = 20? No, 12+8=20, but jumps are 2, 4, 8 — doubling? But let’s check if linear works better.
Actually, try this: 6, 8, ?, 20 — difference between 6 and 20 is 14 over 3 steps → not clean.
Alternative: Maybe it’s +2, then +4, then +8?
6 + 2 = 8
8 + 4 = 12
12 + 8 = 20 → YES! Pattern: add 2, then 4, then 8 (doubling the addend).
So missing is 12
But wait — let’s double-check with simpler idea: maybe it’s arithmetic?
If 6, 8, x, 20 — average step: (20-6)/3 ≈ 4.66 — not integer.
But 6 to 8 (+2), 8 to 12 (+4), 12 to 20 (+8) — yes, powers of 2 added. So 12 is correct.
→ Missing: 12
8. 4, 5, __, 10
4 to 5 is +1. If we do +1 again: 5+1=6, then 6+?=10 → need +4? Not consistent.
Try: 4, 5, ?, 10 — maybe +1, +2, +3?
4 +1 =5
5 +2 =7
7 +3 =10 → YES!
→ Missing: 7
9. 4, 9, 16, __
These are squares!
2²=4, 3²=9, 4²=16, so next is 5²=25.
→ Missing: 25
10. 8, 16, 24, 32, __
Each time +8: 8, 16(+8), 24(+8), 32(+8), so next is 40.
→ Missing: 40
11. 0, 1, 1, 2, 3, 5, __
This is Fibonacci! Each number is sum of two before:
0+1=1, 1+1=2, 1+2=3, 2+3=5, so 3+5=8.
→ Missing: 8
12. 30, 28, 26, 24, __
Decreasing by 2 each time: 30-2=28, 28-2=26, 26-2=24, so 24-2=22.
→ Missing: 22
13. 16, 12, 8, __
16 to 12 is -4, 12 to 8 is -4, so next is 8-4=4.
→ Missing: 4
14. 27, 26, 24, 21, __
27 to 26: -1
26 to 24: -2
24 to 21: -3
So next should be -4 → 21-4=17.
→ Missing: 17
15. 32, 30, 26, 18, __
32 to 30: -2
30 to 26: -4
26 to 18: -8
Pattern: subtracting doubles: -2, -4, -8 → next -16
18 - 16 = 2
→ Missing: 2
16. 500, 100, 20, __
500 ÷ 5 = 100
100 ÷ 5 = 20
20 ÷ 5 = 4
→ Missing: 4
17. 48, 24, 12, __
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
→ Missing: 6
18. 81, 27, 9, __
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
→ Missing: 3
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Final Answer:
1. 6
2. 9
3. 9
4. 10
5. 3
6. 8
7. 12
8. 7
9. 25
10. 40
11. 8
12. 22
13. 4
14. 17
15. 2
16. 4
17. 6
18. 3
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1. 2, 4, __, 8
Look: 2 to 4 is +2. Then 4 to ? should be +2 → 6. Then 6 to 8 is +2. ✔
→ Missing: 6
2. 1, 5, __, 13
1 to 5 is +4. 5 to ? should be +4 → 9. 9 to 13 is +4. ✔
→ Missing: 9
3. 3, 6, __, 12
3 to 6 is +3. 6 to ? should be +3 → 9. 9 to 12 is +3. ✔
→ Missing: 9
4. 5, __, 15, 20
5 to ? to 15 to 20. From 15 to 20 is +5. So before that, ? to 15 should also be +5 → ? = 10. Check: 5 to 10 is +5. ✔
→ Missing: 10
5. 1, __, 9, 27
Hmm… 1 to ? to 9 to 27. Looks like multiplying by 3?
1 × 3 = 3 → 3 × 3 = 9 → 9 × 3 = 27. Perfect!
→ Missing: 3
6. 4, __, 16, 32
4 to ? to 16 to 32. Let’s see: 16 to 32 is ×2. So ? to 16 should be ×2 → ? = 8. Check: 4 to 8 is ×2. ✔
→ Missing: 8
7. 6, 8, __, 20
6 to 8 is +2. If we keep +2: 8 + 2 = 10, then 10 + 2 = 12… but next is 20? That doesn’t fit.
Wait — maybe it’s increasing by even numbers?
6 + 2 = 8
8 + 4 = 12
12 + 8 = 20? No, 12+8=20, but jumps are 2, 4, 8 — doubling? But let’s check if linear works better.
Actually, try this: 6, 8, ?, 20 — difference between 6 and 20 is 14 over 3 steps → not clean.
Alternative: Maybe it’s +2, then +4, then +8?
6 + 2 = 8
8 + 4 = 12
12 + 8 = 20 → YES! Pattern: add 2, then 4, then 8 (doubling the addend).
So missing is 12
But wait — let’s double-check with simpler idea: maybe it’s arithmetic?
If 6, 8, x, 20 — average step: (20-6)/3 ≈ 4.66 — not integer.
But 6 to 8 (+2), 8 to 12 (+4), 12 to 20 (+8) — yes, powers of 2 added. So 12 is correct.
→ Missing: 12
8. 4, 5, __, 10
4 to 5 is +1. If we do +1 again: 5+1=6, then 6+?=10 → need +4? Not consistent.
Try: 4, 5, ?, 10 — maybe +1, +2, +3?
4 +1 =5
5 +2 =7
7 +3 =10 → YES!
→ Missing: 7
9. 4, 9, 16, __
These are squares!
2²=4, 3²=9, 4²=16, so next is 5²=25.
→ Missing: 25
10. 8, 16, 24, 32, __
Each time +8: 8, 16(+8), 24(+8), 32(+8), so next is 40.
→ Missing: 40
11. 0, 1, 1, 2, 3, 5, __
This is Fibonacci! Each number is sum of two before:
0+1=1, 1+1=2, 1+2=3, 2+3=5, so 3+5=8.
→ Missing: 8
12. 30, 28, 26, 24, __
Decreasing by 2 each time: 30-2=28, 28-2=26, 26-2=24, so 24-2=22.
→ Missing: 22
13. 16, 12, 8, __
16 to 12 is -4, 12 to 8 is -4, so next is 8-4=4.
→ Missing: 4
14. 27, 26, 24, 21, __
27 to 26: -1
26 to 24: -2
24 to 21: -3
So next should be -4 → 21-4=17.
→ Missing: 17
15. 32, 30, 26, 18, __
32 to 30: -2
30 to 26: -4
26 to 18: -8
Pattern: subtracting doubles: -2, -4, -8 → next -16
18 - 16 = 2
→ Missing: 2
16. 500, 100, 20, __
500 ÷ 5 = 100
100 ÷ 5 = 20
20 ÷ 5 = 4
→ Missing: 4
17. 48, 24, 12, __
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
→ Missing: 6
18. 81, 27, 9, __
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
→ Missing: 3
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Final Answer:
1. 6
2. 9
3. 9
4. 10
5. 3
6. 8
7. 12
8. 7
9. 25
10. 40
11. 8
12. 22
13. 4
14. 17
15. 2
16. 4
17. 6
18. 3
Parent Tip: Review the logic above to help your child master the concept of algebra 1 sequences worksheet.
